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A Mean Field Competition

Listed author(s):
  • Marcel Nutz
  • Yuchong Zhang
Registered author(s):

    We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable Poissonian model in which we can describe the optimal effort for a given reward scheme. Second, we study the principal--agent problem of designing an optimal reward scheme. A surprising, explicit design is found to minimize the time until a given fraction of the population has reached the goal.

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    File URL: http://arxiv.org/pdf/1708.01308
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    Paper provided by arXiv.org in its series Papers with number 1708.01308.

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    Date of creation: Aug 2017
    Handle: RePEc:arx:papers:1708.01308
    Contact details of provider: Web page: http://arxiv.org/

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    1. Hyeng Keun Koo & Gyoocheol Shim & Jaeyoung Sung, 2008. "Optimal Multi-Agent Performance Measures For Team Contracts," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 649-667.
    2. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    3. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    4. Romuald Elie & Dylan Possama\"i, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    5. Sergey Nadtochiy & Mykhaylo Shkolnikov, 2017. "Particle systems with singular interaction through hitting times: application in systemic risk modeling," Papers 1705.00691, arXiv.org.
    6. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    7. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    8. Cao, Dan, 2014. "Racing under uncertainty: Boundary value problem approach," Journal of Economic Theory, Elsevier, vol. 151(C), pages 508-527.
    9. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
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